Looking at AMS 2431/4 Peening Media (AWS)Conditioned Stainless Steel Cut Wire Shot Section 3.8 this indicates that the weight of 50 pieces of AWS96 should weigh between 3.45 to 4.25 grams.

SAE J441 Cut Wire Shot Table 3 Weight Limits For Condidtioned Cut Wire Shot says the weight for 50 pieces should be between 3.800-4.700 grams

Which is correct?

Actually this is not limited to size 96. All of the sizes have different weight allowances. I believe this is because AMS2431/4 grade material is conditioned more than J441.

Therefore, AMS grade material will be slightly smaller thereby weigh less than J441.

AWS96 3.45 to 4.25 = 0.8 gram tolerance.
SCW96 3.800 to 4.700 = 0.9 gram tolerance.

There are significant differences between J441 and the AMS media specs. See image below or click for pdf image.

I have to ask why does this really matter to the shot peener? It matters to the producer of peening media. However.....
If shot peener puts the as certified media directly into their machine the accept reject criteria is considerably easier and based on sieve analysis not weight measurement. Perhaps poor size quality media was delivered by the supplier, but the users machine would screen this out if done properly. There would be no hardware impact part being peened. However, there may be some loss of media and thereby a cost impact to the user. This would be part of their risk tolerance analysis.